Piezoelectric crystal apparatus



April 29, 1941.

2 sheets-sheet l Filed sept.l 30, 1939 ODSERVER 7 /N VE /V O/ Too /LLATR 0R ricrea c//gcu/r By W P M14 50N 'UJQ ATTORNEY .will

.FREQUENCY/N KILOCVCLES PER SECOND Apri129,1941. w P. MASON V2,240,309

PIEZOELECTRIC CRYSTAL APPARATUS Filed Sept. 50, 1939 2 Sheets-Sheet 2FREQUENCY IN AILOCYCLE'Sv PER SECOND PER CEN TMETER ELEMENMRY LENGTH]ANGLE of' /N nEcREEs (a :45

ANGLE anp /N 0EaREEs(e-45) ANGLE ont /NaEc/aEEs (e: 45') ATTORNEYPatented Apr. 29, 1941 UNTED STATES PA'ENT OFFICE PEEZOELECTRC CRYSTALAPPARATUS Application September Sil, i933, Serial No. '297,259

(El. lil-32'?) le Claims,

This invention relates to piezoelectric crystal apparatus andparticularly to harmonic piezoelectric quartz crystals adapted for useas circuit elements in such systems as electric wave filter systems andradio frequency oscillation generator systems for example.

In my United States Patent No. 2,204,762 granted June 18, 1940, onapplication Serial No.

y180,921=y filed December 2l, 1937, fundamental mode quartz crystalelements of low or substanv tially zero temperature coefficient offrequency are described. In this application, harmonic mode quartzcrystal elements are described which have much the same characteristicsas the fundamental inode crystals referred to.

One of the objects of this invention is to obtain relatively highfrequency piezoelectric crystals of 10W or substantially zerotemperature coefcient of frequency.

Another object of this invention is to obtain "i oscillators which donot vary appreciably with temperature change. For the relatively lowerfrequencies, this requirement is met very well by fundamental modecrystals of the type described in my patent application Serial No.180,921 referred to, but for the relatively higher frequencies, suchfundamental Inode crystals in some instances may be ineonveniently smallin size. It is the purpose of this invention to provide harmonic modecrystals of low or substantially zero temperature coeiiicient offrequency L which are' capable of giving very good stability forfrequencies up to several megacycles per second, the harmonic modequartz crystal elements having such related orientation, dimensionalratio and vibrational mode as to obtain the desired low or substantiallyzero temperature cceficient of frequency Within temperature ranges thatmay occur in practice.

In accordance with this invention, a relatively thin piezoelectricquartz crystal plate of suitable CTL orientation With respect to the X,Y and Z axes thereof, and of a suitable dimensional ratio correspondingto the orientation, may be subjected to a thickness direction or Yelectric eld and vbrated at an odd or an even harmonic resonancefrequency dependent mainly upon the longest or major axis lengthdimension of the crystal plate in a coupled mode of motion whichconsists of an harmonic longitudinal or extensional vibration along suchlength dimension giving the harmonic resonance frequency referred to andmechanically coupled therewith transverse vibrations along the widthdimension of the substantially rectangular major plane of the crystalplate. The width or transverse vibrations referred to are in the natureof edge bulge vibrations alternately bulging outwardly and inwardly theopposite elementary portions of the longest edges of the crystal plate.The orientation of the crystal plate may be any of several, the majoraxis or length dimension of the crystal plate being in every such caseinclined either about 45 or alternatively about 135 degrees with respectto an electric axis X, and

the major plane being in every case parallel or nearly parallel to suchX axis and inclined with respect to the optic axis Z at any anglebetween about 50 and '70 degrees or between about +35 and +70 degrees.Such quartz crystal plates when suitably proportioned as to relativeWidth and length dimensions produce, for the harmonic longitudinal moderesonant frequency mentioned, a low or substantially zero temperaturecoefcient of frequency at temperatures within a temperature rangebetween -40 and +100o C. In a particular species where the major planeof the crystal plate is inclined about +51 degrees with respect to the Zaxis and the fundamental or elementary length of each of the elementaryareas of the harmonic mode crystal plate is related to theabove-mentioned width dimension in the ratio of about 0.86, thelongitudinal mode harmonic resonant frequency referred to has a veryconstant or fiat frequency characteristic throughout a wide range oftemperatures, the mid-temperature of such constant frequency range beingabout +16o C.

To further reduce the temperature coeiiicient of frequency of suchcrystals operating at or near the resonant frequency and having a smalltemperature-frequency coefficient, a condenser of small capacity may beconnected in series circuit relation with the crystal, the condenseritself having a temperature coeflicient of capacitance of such magnitudeand saine sign as that for the crystal, the result being that it willbalance that of the resonant frequency of the crystal thereby reducingthe over-all temperature coefficient of frequency of the combination.

For a clearer understanding of the nature of this invention and theadditional features and objects thereof, reference is made to thefollowing description taken in connection with the accompanyingdrawings, in which like reference characters represent like or similar'parts and in which:

Figs. l and 2 are greatly enlarged views of an harmonic modepiezoelectric quartz crystal plate embodying this invention, Fig. 1being a projected edge view taken in the horizontal direction indicatedby the arrows I--I of Fig. 2 and Fig. 2 being a, major face View takenin the direction indicated by the arrows Z--2 of Fig. l;

Fig. 3 is a major face View of a quartz plate similar to that of Fig. 2but having an alternative i5-degree orientation angle with respect tothe X axis;

Fig. 4 is an edge View of the crystal plate of Figs. 1 to 3 providedwith electrodes and electrode connections for fifth harmonic modeoperation, and a condenser connected in series circuit relation with thecrystal plate;

Fig. 5 is a graph showing the calculated relation between theorientation angle and the resonant frequency of quartz crystals inaccordance with this invention;

Figs. 6 and 7 are graphs showing the relation between the orientationangle and the dimensional ratio of quartz crystals in accordance withthis invention, the dimensional ratios being plotted against values of pfor 6:45 degrees and representing those dimensional ratios which, forthe various angles represented by these curves, give zero or lowtemperature cocilicicnt of frequency;

Fig. 8 is a graph showing ie relation between the orientation angle, theresonant frequency and the temperature range of quartz crystals inaccordance with this invention for p angles in the region ofsubstantially +51 degrees, the frequencies being plotted against valuesof p for :45 degrees and representing those frequencies which, for theangles represented by the curve,

have zero or low temperature coeicients when the dimensional ratios arethose given by the curve of Fig. 9 for the corresponding angle. Thecurve of Fig. 8 represents that part of the curve of Fig. in the regionof p:+51 degrees but drawn to larger scale; and

Fig. 9 is a graph showing the relation between the orientation angle,the dimensional ratiov and the temperature range of quartz crystalsembodying this invention for o angles in the region of substantially +51degrees, the dimensional ratios being plotted against values of c for0:45 degrees and representing those dimensional ratios which, for theangles represented by the curve, give zero temperature coefficient offrequency. The curvev of Fig. 9 represents that part of the curve of 7in the region of o:+51 degrees d-.awu to larger scale.

This speciiication follows the conventional terminology as applied tocrystalline quartz which l. three orthogonal or mutually perpennr X, Yand Z as shown in the drawto desifr .ate an electric. a mechanical andthe optic a: s. respectively. of piezoelectric quartz crystal materal,and which employs three orl'iogonal axes Y and Z to designate thedirections of axes of a piezoelectric body angularly oriented withrespect to such X, Y and Z axes thereof. Where the orienta-tion isobtained by double rotations of the quartz crystal element I, onerotation being in eiiect substantially about an electric axis X, and theother about another axis of the piezoelectric body as illustrated inFigs. l and 2, the orientation angles (p and 0 respectively, designatein degrees the eective angular .position of the crystal plate I asmeasured from the optic airis Z and from the orthogonal electric anis X,respectively. The axis X" shown in Figs. 2 and 3 indicates the result cia second rotation.

Quartz crystals may occur in two forms, namely, right-handed andleft-handed. A righthanded quartz crystal is one in which the plane ofpolarization of a plane polarized light ray travcling along the opticairis Z in the crystal is rotated in a right-hand direction, orclockwise as viewed by an observer located at the light source andfacing the crystal. This definition of righthandcd quartz follows theconvention which originated with Herschel. Trans. Cain. Phil. Soc. Vol.1, page 43 (1821); Nature Vol. 110, page 807 (1922); Quartz Ptesonatorsand oscillators, P. vigoureux, page l2 (1931), Conversely, a quartzcrystal is designated as left-handed if it rotates such plane ofpolarization referred to in the lefthanded or counter-clockwisedirection, namely, in the direction opposite to that given hereinbeforefor the right-handed crystal.

If a compressional stress or a squeeze be applied to the ends of anelectric axis X of a quartz body l and not removed, a charge will bedeveloped which is positive at the positive end C+) or the X axis andnegative at the negative end of such electric axis X, for eitherrighthanded or left-handed crystals. The magnitude and sign oi thecharge may be measured in a known manner with a vacuum tube electrometerfor example. In specifying the orientation of a right-handed crystal,the sense of the angle (p which the new axis Z makes with respect to theoptic axis Z as the crystal plate is rotated in elect about the X axisis deemed positive when, with the compression positive end of the X axispointed toward the observer, the rotation is in a clockwise direction asillustrated in Fig. l. A counter-clockwise rotation of such aright-handed crystal about the X axis gives rise to a negativeorientation angle :p with respect to the Z axis. Conversely, theorientation angle oi' a left-handed crystal is positive when, with thecompression positive end (-1-) of the electric axis X pointed toward theobserver, the rotation ls counter-clockwise, and is negative when therotation is clockwise. The crystal material illustrated in Figs. 1 to 3is right-handed as the term is used herein. For either right-handed orlefthanded quartz, a positive angle o rotation of the Z axis withrespect to the Z axis as illustrated in Fig. l is toward parallelismwith the plane of a miner apex face oi the natural quartz crystal, and anegative o angle rotation o! the Z axis with respect to thc Z axis istoward parallelism with the plane oi a nia-jor apex face of the naturalquartz crystal.

Referring to the drawings, Figs. 1 and 2 are respectively an edge viewand a major face view of a right-handed relatively thin piezoelectricuartz crystal plate I of substantially rectangular parallelepiped shapehaving an over-all length dimension L, a` width dimension W which isperpendicular to the length dimension L, and

a thickness or thinnest dimension T which is perpendicular to the lengthdimension L and the Width dimension W. As shown in Fig. 1, the majorplane and the opposite major faces 2 and 3 :of the crystal plate I maybe parallel or nearly parallel to an electric or X axis of the quartzmaterial and inclined with respect to the optic axis Z at a (p angle ofabout +51 degrees as measured between the Z and Z axes in a plane whichis perpendicular to the X axis and to the major plane of the crystalplate I. Small angle departures up to 5 degrees or more, for example ofthe major faces 2 and 3, from parallelism With respect to the X axis donot greatly alter the corresponding q; angle required to obtain the lowor substantially zero temperature coefficient of frequency. Since theminor apex faces of the natural quartz crystal from which the quartzplate I is cut occur at a p angle of about +38 degrees with respect tothe optic axis Z, the positive sense for the fp angle is equivalent to arotation about the X axis from the Z axis toward parallelism with theplane of a minor apex face for either right-handed or left-handedquartz.

In Fig. 1, the X axis is perpendicular to the plane of the drawing withthe compression positive end (-I) of the X axis pointed towards theobserver, and is also perpendicular to both the Y and Z axes. Theover-all length dimension L of the crystal plate I lying along the majoraxis X as shown in Figs. 2 and 3 may be inclined at an angle 0 of about45 degrees with respect to the above-mentioned X axis in eitherdirection as illustrated by the alternative 6 angle orientations shownin Figs. 2 and 3. While the major axis length dimension L of the crystalplate I of Fig 2 is inclined at a different 45-degree 0 angle withrespect to the X axis than that of Fig, 3, it Will be understood thateither of these 45-clegree posi tions for the angle 0 may be usedalternatively with any of the p angles disclosed herein.

Suitable conductive electrodes such as the electrodes 4 in Figs. 2 and 4may be placed on, adjacent or be formed integral With the opposite majorfaces 2 and 3 of the crystal plate I to apply harmonic mode electricfield excitation to the quartz plate I in the direction of the thicknessdimension T, and by means of any suitable circuit such as, for example,a filter or an oscillator circuit, the quartz plate I may be vibrated inthe desired longitudinal mode of motion at an odd or an even harmonicvibration response frequency which depends mainly upon and variesinversely as the major axis length dimension L and the elementary lengthdimension Z. It will be understood that the crystal plate I may beoperated in any desired odd or even harmonic mode along the lengthdimension L by means of a plurality of pairs of equal area oppositeelectrodes disposed adjacent the opposite major faces 2 and 3 of thecrystal plate I. The electrodes may be interconnected as illustratedschematically in Fig. 4 so that all positive electrodes are connectedtogether and all negative (e) electrodes are connected together but nopositive electrode is connected with a negative electrode. The number ofpairs of opposite electrodes to be used corre sponds to the numericalorder of the desired harmonic which may be any odd or even overtone ofthe fundamental mode. For example, to drive the crystal I in the fifthharmonic longitudinal mode, ve pairs of equal area opposite electrodes 4may be utilized as illustrated in Figs. 2 and 4; and similarly to drivethe crystal plate I in third harmonic longitudinal vibrations along thelength dimension L, three pairs of opposite electrodes which may partlyor nearly Wholly cover the equal elementary lengths l of the major faces2 and 3 may be utilized. The odd harmonic mode is of special interestsince then the crystal plate I may b-e clamped at its geometrical center6 at the centers of the middle pair of opposite electrodes. Reference ismade to my United States Patent No. 2,185,599 granted January 2, i940,on application Serial No. 65,922, filed February 2l, 1936 for examplesof harmonic mode electrode and electrode connection arrangements thatmay be utilized to drive any of the crystal plates described herein inharmonic mode longitudinal vibrations along the major axis lengthdimension L. These harmonic mode electrode and connection platings maybe such as to leave three edges of the crystal body entirely free of anyplating in order to make edge grinding adjustments of the frequency andthe temperature coefficient of frequency,

The harmonic mode crystal plates described herein may be mounted in anysuitable manner such as, for example, by clamping the electroded crystalplate i between a pair of opposite conductive clamping projections 5which may contact the electroded crystal plate i at opposite points ofvery small area designated il in Figs. 2 and 4. As an illustrativeexample, an evacuated holder of the type disclosed in United StatesPatent No. 2,203,486 granted June 4, 1940, on application Serial No.248,487, filed December 39, 1938 by W. L. Bond may be utilized for thispurpose.

Alternatively, the elec'trcded crystal plate i may be supported bysoldering or otherwise attaching electrically conductive spring wires,to any pair such as the middle pair of the crystal electrodes 4, at theopposite points designated El in Figs. 2 and 4. Such Wires may supportand hold the electroded crystal plate I in spring suspension.

lt will be understood that any holder which Will give stability and arelatively high reactanceresistance ratio, Q, may be used to mount theseharmonic mode crystals.

The desired resonant frequency of the harmonic mode crystal plate l is afunction of the major axis length dimension L and of the several equalelementary or fundamental lengths Z, the over-all length L being equalto the 1i times the elementary length dimension l Where 1r is thenumerical order of the harmonic as determined by the number of pairs ofopposite electrodes that are applied to the major faces 2 and 3 of thecrystal plate I of any o angle. Since the invention may be adapted toany order of harmonic operation, odd or even, the correlated values offrequency and dimensional ratio corresponding to the p angle selected,are given hereinafter in terms of the Width dimension W and theelementary length dimensions Z. It will he noted that in so far as theelementary areas are concerned, the related values of the orientation,the dimensional ratio and the frequency constant of the severalelementary ar as cf the harmonic mode crystals of this applicationfollow those values given for the fundamental mode crystals of thecorresponding orientation described in applica tion Serial No. 180,92ireferred to, and also that the mechanical coupling between the harmonicm-ode longitudinal vibrations along the major axis length dimension Land the vibrations along the Width dimension W of these harmonic modecrystals I is as strong as it is when both vibrations are fundamentalmode as in the application Serial No. 180,921 referred to.

Fig. 5 is a graph giving the calculated values of frequency inkilocycles per second per centimeter of elementary length dimension l ofthe crystal plate I for all angles of p from -90 to +90 degrees, theangle being always equal to 45 (or .135) degrees for every angle of fp.For any given angle of :p the curve of Fig. gives the approximatefrequency constant corresponding thereto in terms of frequency inkilocycles per second per centimeter of the elementary length dimensionof the crystal plate 1 or n times this value where n is the numericalorder of the harmonic frequency. Since the frequency of the longitudinalmode vibrations along the length Z varies inversely as the particularlength dimension of l involved, the Value of l in centimeterscorresponding to the resonant frequency in kilocycles per second may beobtained directly from the frequency constant given by the curve of Fig.5 for any value of the angle p selected. These cal-culated values ofresonant frequency approximate the measured values.

I'lie curves' of Figs. 6 and 7 give the orientation angles of p and thecorresponding dimensional ratios that may be used to construct quartzplates to obtain a low or substantially zero temperature coemcient offrequency. The dimensional ratios are therein given in terms of thewidth dimension W and the fundamental or elementary length dimension lof the crystal plate I, the elementary length dimension Z of each of theelementary areas of the crystal plate being equal to L/n where L is themajor axis over-all length dimension of the crystal plate I and n is thenumerical order of the harmonic such as the second, third, fifth, etc.harmonic. The curve of Fig. 6 gives the dimensional ratios in terms ofthe width W with respect to the elementary length l for all of thecorresponding negative angles of (p between about 50 and -70 degreeswhile the curve of Fig. 7 gives' the dimensional ratios in terms of theelementary length Z with respect to the width W` for all of thecorresponding positive angles of e between about and +70 degrees, theangle 0 in every case being about 45 degrees as illustrated in eitherFig. 2 or Fig. 3. The angles of fp outside of these ranges as given inFigs.

6 and 7 do not produce the substantially Zero temperature coefficient offrequency.

The corresponding frequency constants for the quartz plates I, orientedand dimensioned in accordance with the values given by the curves ofFigs. 6 and 7 are substantially given by the curve of Fig. 5 at theintercept of the particular value of e selected. For example, when gp issubstantially +51 degrees, 0 being substantially degrees, and thedimensional ratio of the elementary length Z with respect to the width Wof the quartz plate I is substantially 0.86 as indicated by the curvesof Figs. 7 and 9, the frequency constant is about 329 kilocycles persecond per centimeter of elementary length dimension l or n times thisvalue per centimeter of over-all length dimension L where n is thenumerical order of the harmonic involved such as 2, 3, 5, etc. Forexample, a fifth harmonic quartz crystal plate I of such an orientationand dimensional ratio and of one centimeter over-all length L will havea resonant frequency of about five times 329 or about 1645 kilocyclesper second which remains substantially constant throughout a wide rangeof temperatures, the mid-temperature of the constant frequencytemperature range being about +16o C. as shown by the curves of Figs. 8and 9.

Other values of corresponding orientation, dimensional ratio andfrequency for crystal plates I that give a low or substantially zerotemperature coefficient of frequency may be obtained from the curves ofFigs. 5, 6 and 7 for any angle of go selected between about +35 and +70degrees or between about and -70 degrees.

It will be noted that for the positive angles of ip, these harmonic typecrystals of low or substantially zero temperature coeflicient offiequency have a width dimension W slightly larger than the length Z ofthe fundamental element of the crystal plate. For example, fifthharmonic mode crystal plates of a positive o angle of +51 degrees have atotal length L a little less than 5 times the width dimension W of thecrystal; while for negative angles of p, fifth harmonic mode crystalshaving negative c angles between 50 and degrees have an over-all lengthdimension L that is a little greater than 5 times the width dimension W.

The curves of Figs. 8 and 9 illustrate the corresponding values ofresonant frequency, dimensional ratio and orientation angle that may beused in the p angle region of +51 degrees to obtain harmonic mode quartzcrystal plates I giving a very constant frequency characteristic aboveand below the mean or mid-temperature values from about 0 to 50 C. whenused in a circuit which operates the crystal plate I at or near itsresonant frequency such as for example an oscillator circuit of the typedisclosed in United States Patent No. 2,163,403, granted June 20, 1939,to L. A. Meacham and discussed in a paper published by L. A. Meacham inThe Proceedings of the Institute of Radio Engineers, vol. 26, No. 10,October 1938, page 1278. When the crystal plate is used in thegrid-filament circuit of a non-inductively coupled Pierce oscillatorcircuit, the values given are nearly the same since this circuit alsooperates the crystal near its resonant frequency and hence produces thenearly nat or constant frequency-temperature relationship.

When used in such circuits which operate the crystal plate I at or verynear the harmonic mode resonant frequency, for angles of p in the regionof substantially +51 degrees 7 minutes, the characteristic curve of theharmonic mode longitudinal resonant frequency as a function oftemperature is substantially flat throughout a wide range oftemperatures in the region above and below about 16 C.; while for anglesof e outside the region of +51 degrees but within the p angle regionsfrom about -50 to 70 degrees and +35 to +70 degrees, the characteristiccurves of frequency as a function of temperature are more or lessparabolic somewhere within the range of temperatures between 50 and+100o C.

When the crystal element is driven, as described in the harmonic modelongitudinal vibrations along the length dimension L by means of anumber of pairs of opposite electrodos corresponding in number of pairsto the order of the harmonic with suitable interconnectionstherebetween, the resulting vibrations consist of liarrnoniclongitudinal or extensional vibrations set up along the length dimensionL of the crystal plate I which tend to set up vibrations also along thewidth dimension W of the crystal element. The force system so set up isfavorable for the so-called bulge type of vibration and hence thepossibility exists that the vibration along the width dimension W whichis mechanically coupled to the harmonic longitudinal vibration along themajor axis length L is a bulge vibration when the elementary face areais square or nearly so as when the dimensional ratio of L/n with respectto the width W is about 0.86. There is a strong coupling between suchwidth vibrations and the harmonic longitudinal vibration resonantfrequency. Accordingly, for an angle of c, the mode of vibration isdescribed herein as a coupled mod-e consisting of longitudinal harmonicmode vibrations along the length dimension L coupled with edge bulgemode vibrations along the width dimension W. The frequency constants forthe harmonic longitudinal mode are given in Fig. for every angle of goand approximate the measured values. Those given in Fig. 8 are moreprecisely stated for angles of p in the region of substantially +51degrees.

The dimensional ratio of the crystal plates described, operates toproduce the low or substantially zero temperature coefficient offrequency at a given temperature and the orientation angle q controlsthe slope of the temperature-frequency characteristic, the slope beingnearly horizontal and flat in the o angle region of substantially +51degrees. It will be noted that for crystals having an angle of fp ofabout +51 degrees, a 0 angle of about l5 degrees and a dimensional ratioof about 0.88 for the elemental length l with respect to the width W.the frequency constant is about 329.4 kilocycles per second percentimeter of elemental length dimension l or 5 times this value for thefifth harmonic cf the longitudinal vibration along the length L. Thus afifth harmonic crystal plate l having a length dimension L of 28.78millimeters, a width W of about 6.59 millimeters and a thickness ofabout 1.0 millimeter will have a fifth harmonic resonant frequency ofabout 580,800 cycles per second.

By a slight change in the o angle of +51 degrees and in thecorresponding dimensional ratio, the mid-temperature of the constantfrequency temperature range may be shifted and raised or lowered asdesired. For example. as shown in Figs. 8 and 9, when the angle cp isabout +51 degrees and minutes, the dimensional ratio of the elementarylength l with respect to the width W about 0.855, and the frequencyabout 328.8 kilocycles per second per centimeter of elementary length l,then the mid-temperature of the constant frequency temperature range isabout +D C.; where the angle go is about +51 degrees '7 minutes, thedimensional ratio of the elementary length l to the width W about 0.859,and the frequency constant about 329.2, the midtemperature of theconstant frequency temperature range is about +25 C. Other values ofcorresponding dimensional ratio and frequency constant as a function ofthe angle qi and the mean temperature of the constant frequencytemperature range may be similarly obtained from the curves of Figs. 8and 9.

The frequency and the temperatur-e coefficient of frequency of any ofthese crystal plates may be adjusted to relatively precise values byedge grinding on the edges along the width W and length L of the crystalplate. Since the frequency is Controlled mainly by the major axis lengthdimension L, the frequency of a slightly oversize crystal plate may beincreased by grinding on either of the edges perpendicular to the lengthdimension L thereby reducing the length dimension L and increasing thefrequency to a value a few cycles under the desired frequency. Then bygrinding on either of the longest edges All perpendicular to the Widthdimension W, the width dimension W may be uniformly reduced therebychanging the dimensional ratio of each of the elementary areas of thecrystal plate l until the desired lowest value of the temperaturecoefficient of frequency is obtained. The frequency will have beenraised slightly by this last step of reducing the width dimension W. Ifthe frequency is still too low, it may be slightly raised by againreducing the length dimension L, and then the width dimension W may beagain readjusted to obtain the desired lowest value of temperaturecoefficient of frequency. By this process of edge grinding, both thefrequency and the temperature coeiiicient of frequency of the crystalplate i may be ultimately adjusted to the correct or desired values. Inaddition to these adjustments, the frequency if too high may be loweredslightly by slightly concaving either of the major faces 2 or 3 of thecrystal plate l along the width dimension W midway between the ends ofany of the elementary lengths Z; and the temperature coeicient offrequency may be lowered and rendered more negative by slightlyconcaving either of the major faces 2 or 3 centrally along the entiremajor axis length dimension L.

The temperature coefficient of frequency and the frequency of thesecrystals having a c angle in the region of +51 degrees may be soadjusted that their temperature coefficients of frequency are less than1 part in 10 million per degree centigrade and that their frequency iswithin 5 parts in a million. Using such crystals in an oscillatorcircuit of the type described in United States Patent No. 2,163,403granted on June 20, 1989, to L, A, Meacham, the frequency of suchoscillators may be held to 1 part in a million without temperaturecontrol and to l part in 10 million with a rough temperature control.After the initial aging period which may be of several months, the longperiod accuracy may be of the same order of magnitude. Such oscillatorsare useful in single side-band radio systems, in broadcast systems, andfor many other purposes.

These harmonic mode crystals of low or substantially zero temperaturecoefficient of frequency may be used in wide band lters at radiofrequencies up to 2 megacycles per second or morey with substantialfreedom from troublesome subsidiary or extraneous resonances. Wide bandquarta crystal filters have heretofore been limited to about 500kilocycles per second due to the extra resonances existing in highfrequency crystals. In carrier systems, it is often desirable to havehighand low-pass filters of very sharp selectivity for the purpose ofdropping off supergroups at intermediate points and hence to havecrystals which can be used in wide band filters at frequencies up to 2megacycles per second or more and which have relatively low impedance,low temperature coefficient of frequency, and vibrate at highfrequencies with the desired frequency of vibration separated as much aspossible from the frequencies of other modes. Any nearby undesiredresonance that is present may, if caused by a flexure mode determined bythe thickness dimension T of the crystal plate l, be removed by changingthe ratio of the thickness dimension '1 with respect to the lengthdimension L, without changing the desired resonance frequency or thetemperature coefcient of the crystal. Otherwise, the thickness dimensionT of the crystal plate i may ordinarily be of the order of 1 millimetermore -or less for example, or of other value to suit the impedance orother requirements of the particular circuit with which it may beassociated.

Either third harmonic or fifth harmonic crystals, for example, may beused to advantage in oscillators or moderately high impedance filters.Assuming a thickness dimension T of about 0.4 millimeter, the inductancein the equivalent circuit of the crystal for the third and iiftliliarmonic frequencies will be respectively 2.35 henries and 1.56 henriesindependent of the frequencies. Such crystals may be used in oscillatorsystems or in lter systems up to 3 megacycles per second, for example.

In the construction of crystals such as the harmonic mode crystal plateshaving a p angle in the region of +51 degrees, as describedhereinbefore, it is often difficult and expensive to adjust thetemperature coefficient of frequency thereof closer than 1 part in 10million per degree centigrade by mechanical adjustments alone on thecrystal itself. When used in an oscillator which is not temperaturecontrolled, such crystals may cause a change in frequency of il part ina million if the temperature changes by i10 C., Which change infrequency may be too large a variation for some purposes. By using aneleca trical element which Varies its impedance with temperature change,the temperature coeicient of frequency of the crystal circuit may becontrolled and adjusted to a value considerably less than 1 part in 10million for i153" C. change in temperature, and over-al1 variations inthe frequency of an oscillator that may be associated therewith may beconsiderably reduced.

For this purpose, as illustrated in Fig. 4, a condenser 'l may beconnected in series circuit relation with the electroded crystal plate Ito still further reduce the temperature coefficient of the desiredresonant frequency of the crystal plate I. The condenser I may have asmall capacitance of the order of 150 micro-microfarads more or less,for example, and of itself have a temperature coefficient of capacitanceof such magnitude and the saine sign as to balance that of the crystalplate and thereby reduce the over-all temperaa ture coefficient offrequency of the combination crystal element and condenser to anextremely small value. As an example, the condenser 1 may consist of oneor more Ceramicon series connected condensers having a suitablecomposite temperature coefficient of frequency and capacitance. TheseCeramicon condensers are readily obtainable on the market with bothpositive and negative temperature coefficients of frequency. Using sucha condenser having a temperature coeflicient of -800 parts in a millionper degree centigrade, for example, negative temperature coefficients offrequency up to about 2.5 parts in 10 million per degree centigrade ineither fundamental mode or harmonic mode crystal plates of p angles inthe region of +51 degrees may be adjusted to very nearly zerotemperature coefficient of frequency for the combined crystal and seriesconnected condenser arrangement. Similarly, using a condenser having atemperature coefcient of +250 parts in a million per degree centigrade,for example, positive temperature coefficients of capacitance up toabout +0.08 part in 10 million per degree centigrade or less in suchcrystal plates may be adjusted to very nearly zero over-all temperaturecoefficient of frequency.

The construction of such Ceramicon condensers of ceramic dielectricmaterial may be roughly described as follows: These Ceramiconcondensei's use as a dielectric either titanium dioxide, which has ahigh negative temperature coefficient of dielectric constant and a highdielectric constant, or talc which has a positive temperaturecoeiiicicnt of dielectric constant and lower dielectric constant. Bymixing the relative proportions of the two materials, a condenser can beobtained which has a temperature c0- efrlcient of capacitance varyingfrom -800 parts per million per degree centigrade to +250 parts permillion per degree centigrade.

The temperature coefficient of the resonant frequency of a combinationcrystal I and a condenser 'I connected in series therewith is given bythe expression:

cierre,

Where Co is the static capacity of the crystal, 1 its ratio ofcapacities, CA the temperature variable capacity, Tc the temperaturecoefficient of frequency of the crystal,

l FCA the temperature coeflicient of the capacity CA, and Ti; thetemperature coefficient of frequency of the combination crystal andcapacity element.

The maximum effect on the temperature coefficient of frequency willoccur when C0=CA as may be seen from the equation. Hence with thecondenser referred to having a negative temperature coefficient offrequency of 800 parts per million per degree centigrade for the Valueof TCA the maximum effect of such a series connected condenser will beto raise the combined temperature coefficient of frequency by 0.25 partper million per degree centigrade as previously stated. Similarly, forthe positive coefficient condenser of +250 parts referred to, thecombined temperature coerTicient of frequency will be lowered by 0.0782part as previously stated.

The measured reactance-resistance ratio Q of these Ceramicon condensersreferred to is of the order of 900 at kilocycles per second but thecombined Q of the combination crystal and condenser is not greatlyaffected by the low value of Q for the condenser at resonant frequency.For example, Where the Q of the original crystal is of the order of100,000, the maximum effect of such a series connected condenser wouldbe to lower it by about '7 per cent.

With a fixed value of temperature coeliicient of frequency Tk: To

TCA

for the condenser, the composite temperature coefficient of frequency ofthe series connected crystal and condenser may be varied by varying thevalue of capacity CA of the condenser.

The frequency will be raised somewhat by putting the condenser 7 inseries with the crystal I. As an illustrative example, a fundamentalmode GT crystal having a p angle of substantially +51 degrees, mountedin a sealed and evacuated container, and operated in a bridge oscillatoras disclosed in United States Patent No. 2,163,403, granted June 20,1939, to L. A. Meacham, had a negative temperature coefficient offrequency of about 0.191 part per million per degree centigrade, afundamental mode frequency of 100,003.8 cycles per second, a staticcapacity of 59 micro-microfarads, a ratio of capacities of 403, aresistance at resonance of ohms, and a value of Q=87,100. By using anegative temperature coefficient of frequency condenser of 1'70micro-microfarad capacity connected in series circuit relation with suchcrystal plate and sufficient inductance placed in series therewith tobring the frequency. of the bridge oscillator to 100 kilocycles persecond, the over-al1 temperature coefficient of frequency was changed toan average value of +0.0045 part per million per degree centigrade whichis very close to zero, the impedance of the crystal was raised somewhat,and the frequency was raised about 30 cycles per second but thereactance-resistance ratio Q of the crystal remained nearly the same,and frequency stabilities of the order of 1 part in 10 million perdegree oentigrade were obtained without temperature control when thiscrystal-condenser combination was used in a bridge oscillator of thetype disclosed in United States Patent No. 2,163,403 to L. A. Meacham.

It will be understood that the condenser l may consist of a plurality ofcondenser units. For example, a condenser of nxed capacity may beconnected in series circuit relation with the crystal I. The frequencyof the crystal will always be changed the same amount by such a seriesconnected condenser. The temperature coefficient of frequency may thenbe adjusted by adding the correct ratio of positive .and negativetemperature frequency coeincient condensers. For example, if a 200micro-microfarad capacity is connected in series circuit relation withthe crystals, then temperature coefcients of frequency of 0.175 and+0.055 therein may be adjusted to nearly aero by utilizing a seriesconnected condenser having temperature coeiicients of frequency of --800or +250 parts per million per degree centigrade respectively. For anyother temperature coefficients of frequency, the adjustment may beeffected by choosing the proper ratio of negative coefficient topositive coefficient condenser. It will be understood that the 100kilocycle per second crystal referred to may itself be adjusted about 30cycles per second under the desir-ed 100 kilocycle per second value andits temperature coefficient of frequency adjusted to nearly zero by theuse of the series connected temperature variable condenser. By suchadjustment of the frequency of the crystal itself to a proper valuebelow the desired frequency, the series-'connected inductance coil maybe eliminated, and the frequency brought to its desired value by meansof the condenser l.

This method for compensating the temperature coeicients of frequency ofcrystals by the use of series-connected temperature variable condensersmay be used to obtain a very nearly zero overall temperature coefficientof frequency for the combined crystal and condenser when used with acrystal which has a temperature coefficient of frequency lying betweenabout 0.25 .and +0.08 parts per million per degree centigrade, forexample, and when it is desired to keep the frequency of the systemwithin about 1 part in 10 million per degree centigrade Without the useof temperature control apparatus. Such temperature coefficients offrequency ranging from about +0.25 to +0.08 part per million per degreecentigrade exist in the crystals described herein when the p angle is inthe region of +51 degrees as illustrated in Fig-s. 8 and 9.

It will be understood that such series connected condenser apparatus isuseful in reducing the temperature coeicient of frequency of theharmonic mode crystals described in this application, the fundamentalmode crystals described in my application Serial No. 180,921 now U. S.Patent 2,204,762 dated June 18, 1940, or any other crystal of low orsubstantially zero temperature coefficient of frequency that is operatednear its resonant frequency.

A small trimmer condenser of suitable capacity say, for example, of theorder of 20 micro-microfarads more or less may be connected in parallelcircuit relation with the electrode terminals. 5 of the crystal elementI to adjust the frequency thereof to the desired final value. As anillustrative example, such a consender may consist of a thin mica sheethaving conductive material such as silver or other suitable conductivematerial deposited in a known manner upon the opposite major surfacesthereof. The adjustment of capacitance may be made by scraping off orotherwise removing part of the silver coating until the desired valuesof capacitance and frequency are obtained.

Although this invention has been described and illustrated in relationto specific arrangements, it is to be understood that it is capable ofapplication in other organizations and is, therefore, not to be limitedto the particular embodiments disclosed, but only by the scope of theappended claims and the state of the prior art.

What is claimed is:

l. A piezoelectric quartz crystal vibratcry body having its oppositesub-stantially rectangular major faces substantially parallel to an Xaxis and inclined substantially +51 degrees with respect to the Z axisas measured in a plane substantially perpendicular to said major faces,the major axis over-all length dimension and the width dimension of saidmajor faces being inclined substantially 45 degrees with respect to saidX axis, said over-all length dimension being in effect divided into aplurality of equal length elementary lengths to form a plurality ofelementary areas, each of said elementary lengths having a dimensionalratio of substantially 0.86 with respect to said width dimension.

2. A piezoelectric quartz crystal vibratory body having its oppositesubstantially rectangular major faces substantially parallel to an Xaxis and inclined substantially +51 degrees with respect to the Z axisas measured in a plane substantially perpendicular to said major faces,the major axis over-all length dimension and the width dimension of saidmajor faces being inclined substantially 45 degrees with respect to saidX axis, said over-all length dimension being in effect divided into aplurality of equal length elementary lengths to form a plurality ofelementary areas, each of said elementary lengths having a dimensionalratio of substantially 0.86 with respect to said width dimension, the'number of said elementary lengths being one of the integers 2 to 5.

3. A piezoelectric quartz crystal vibratory body having its oppositesubstantially rectangular major faces substantially parallel to an Xaxis and inclined substantially +51 degrees with respect to the Z axisas measured in a plane substantially perpendicular to said major faces,the major axis over-all length dimension and the width dimension of saidmajor faces being inclined substantially 45 degrees with respect to saidX axis, said over-all length dimension being in -effect divided into aplurality of equal length elementary lengths to form a plurality ofelementary areas, each of said elementary lengths having a dimensionalratio of substantially 0.86 with respect to said width dimension, andelec-V trodes adjacent each ol' said elementary areas of said majorfaces of said crystal body.

4. A piezoelectric quartz crystal vibratory body having its oppositesubstantially rectangular major faces substantially parallel to an Xaxis and inclined substantially +51 degrees with respect to the Z axisas measured in a plane substantially perpendicular to said major faces,the major axis over-all length dimension and the Width dimension of saidmajor faces being inclined substantially 45 degrees with respect to saidX axis, said over-all length dimension being in effect divided into aplurality of equal length elementary lengths to form a plurality ofelementary areas, each of said elementary lengths having a dimensionalratio of substantially 0.86 With respect to said Width dimension, meansincluding electrodes adjacent said elementary areas of said major facesfor operating said crystal body in harmonic mode vibrations at aresonant frequency of low temperature coefficient, and a condenserconnected in series circuit relation with said electroded crystal body,said condenser having a temperature coeicient of capacitance of a valuesuflicient to reduce said low temperature coefficient of frequency ofsaid crystal body.

5. A piezoelectric quartz crystal vibratoi'y body having its oppositesubstantially rectangular 1na jor faces substantially parallel to an Xaxis and inclined substantially +51 degrees with respect to the Z axisas measured in a plane substantially perpendicular to said major faces,the major axis over-al1 length dimension and the width dimension of saidmajor faces being inclined substantially 45 degrees with respect to saidX axis, said over-all length dimension being in effect divided into aplurality of equal length elementary lengths to forni a plurality ofelementary areas, each of said elementary lengths having a dimensionalratio of substantially 0.86 with respect to said width dimension, andmeans including electrodes formed integral with said elementary areas ofsaid major faces for operating said crystal bodf,7 in a mode of motionconsisting substantially of harmonic longitudinal vibrations along saidmajor axis length dimension mechanically coupled with transversevibrations along said width dimension.

6. A quartz piezoelectric body of low temperature coefficient offrequency adapted to vibrate at a harmonic frequency dependent mainlyupon the major axis length dimension thereof, said body having a majorplane of substantially rectangular shape, said major plane beingsubstantially parallel to an X axis and inclined with respect to the Zaxis substantially +51 degrees as measured in a plane perpendicular tosaid major plane, said length dimension and the Width dimension of saidmajor plane being inclined substantially 45 degrees with respect to saidX axis, said length dimension arithmetically divided by the numericalorder of said harmonic frequency being related to said width dimensionin the ratio of substantially 0.86.

7. A piezoelectric quartz crystal body adapted to vibrate at a harmonicfrequency dependent mainly upon its major axis length dimension, themajor plane of said body being substantially parallel to an X axis andinclined substantially +51 degrees with respect to the Z axis asmeasured in a plane perpendicular to said major plane, said lengthdimension and the Width dimension of said major plane being inclinedsubstantially 45 degrees with respect to said X axis, said lengthdimension arithmetically divided by the numerical order of said harmonicfrequency being substantially 0.86 of' said width dimension, fre quencybeing substantially 329 kilocycles per second per centimeter of saidlength dimension arithmetically multiplied by said numerical order ofsaid harmonic frequency.

8. A piezoelectric quartz crystal plate having substantially rectangularmajor faces and means including a plurality of pairs of electrodesdisposed adjacent said major faces for operating said crystal plate at aharmonic frequency dependent mainly upon the major axis dimension ofsaid major faces, said pairs corresponding in number to the numericalorder of said harmonic and being disposed along the equal elementarylengths of said major axis dimension, said major faces beingsubstantially parallel to an X axis and inclined substantially +51degrees with respect to the Z axis as measured in a plane perpendicularto said major faces, said major axis of said major plane being inclinedsubstantially 45 degrees With respect to said X axis, the dimensionalratio of each of said elementary lengths with respect to the Widthdimension of said major faces being substantially 0.86.

9. A piezoelectric quartz crystal body of low or substantially zerotemperature coeiiicient of frequency adapted to vibrate at a harmonicfrequency dependent mainly upon each of the fundamental or elementarylength dimensions along the maior axis of said body multiplied by thenumerical order of said harmonic frequency, the major plane of said bodybeing substantially rectangular, disposed substantially parallel to an Xaxis and inclined at an angle within the range substantially from +5flo45 to +51o 30 with respect to the Z axis, said major axis of said majorplane being inclined substantially 45 degrees with respect to said Xaxis, said angle and the corresponding dimensional ratio of each of saidelementary length dimensions with respect to the width dimension of saidmajor plane being substantially those values given by the curve of Fig.9, and the frequency for each of said elementary length dimensions beinggiven by the curve of Fig. 8 at the intercept for said angle.

l0. A piezoelectric quartz crystal body, the major axis length dimensionof said body being divided in effect into equal elementary lengths inaccordance with the numerical order of a harmonic selected to obtainharmonic mode vibrations along said rnajor axis dimension, the majorfaces of said body being substantially rectangular, substantiallyparallel to an X axis and in clined at an angle Within the rangesubstantially from -50 to +70 and from +35 to +70 degrees with respectto the Z axis, said major axis length dimension being inclinedsubstantially 45 degrees with respect to said X axis, the dimensionalratio of said elementary lengths With respect to the Width dimension ofsaid major faces of said body being a selected value, said dimensionalratio, said angle and said frequency being such related values as givenby the curves of Figs. 5, 6 and 7 as to obtain a low or substantiallyzero temperature coefficient of frequency for said harmonic modevibrations.

11. A piezoelectric quartz crystal body of low temperature coefficientof frequency adapted to vibrate in a mode of motion consisting mainly oftwo coupled vibrations, one along the major axis length dimension andthe other along the width dimension of the major plane thereof, and at aharmonic mode frequency dependent upon the elementary length dimensionequal to said major axis length dimension arithmetically divided by thenumerical order of said harmonic, said frequency being given by thecurve of Fig. for the angle corresponding to the angle given by thecurves of Figs. 6 and 7, said major plane being of substantiallyrectangular shape, disposed substantially parallel with respect to an Xaxis and inclined at said angle Within the range substantially from -50te -70 and from +35 to +70 degrees with respect to the Z axis, saidmajor axis of said maior plane being inclined substantially li5 degreeswith respect to said X axis, said angle and the dimensional relationbetween said width dimension and said elementary length dimension beingsubstantially those values given by the curves of Figs. 6 and 7.

12. A piezoelectric quartz crystal body adapted for longitudinalvibrations along and at a harmonic frequency dependent mainly upon theelementary lengths of the major axis length dimension of itssubstantially rectangular major plane, said major plane beingsubstantially parallel to an X axis and inclined at an angle b..- tweensubstantially and +70 degrees with respect to the Z axis as measured ina plane perpendicular to said major plane, said major axis beinginclined substantially degrees with respect to said X axis, thedimensional ratio of each of said elementary or fundamental lengths ofsaid major axis length with respect to the width dimension of said majorplane being between substantially 0.85 and 1.0, said angle and saiddimensional ratio having such relative values as to provide a low orsubstantially zero temperature coefficient for said harmonic frequency.

13. A piezoelectric quartz crystal body adapted for longitudinalvibrations along and at a. harmcnic frequency dependent mainly upon theelementary lengths of the major axis length dimension of itssubstantially rectangular major plane, said major plane beingsubstantially parallel to an X axis and inclined at an angle between anddegrees with respect to the Z axis as measured in a plane perpendicularto said major plane, said major axis being inclined substantially 445degrees with respect to said X axis, the dimensional ratio of the widthdimension of said major plane with respect to each of said elementary orfundamental lengths of said major axis length dimension being betweensubstantially 0.64 and 1.0, said angle and said dimensional ratio havingsuch relative values as to produce a low or substantially zerotemperature coefficient of frequency for said harmonic frequency.

14. A piezoelectric quartz crystal element havits major plane and majorfaces substantially parallel to an X axis and inclined substantially +51degrees with respect to the Z axis, the edges of said major plane beinginclined substantially 45 degrees with respect to said X axis, saidcrystal element having a resonant frequency of low temperaturecoeiiicient of frequency, electrodes adjacent said major faces, andmeans including a condenser connected in series circuit relation withsaid crystal element for reducing said low temperature coeflicient offrequency of said crystal element.

WARREN P. MASON.

